AP-domains and unique factorization.
type: Item
instance of: scholarly article
title: AP-domains and unique factorization.
zbMATH Open document ID: 1086.13007
author: Muhammad Zafrullah
author: Jim Coykendall
published in: Journal of Pure and Applied Algebra
publication date: 2004-07-12T00:00:00Z
review text: Let \(R\) be a domain and \(\pi \in R\) an irreducible element which is not prime. The authors construct a domain \(T \supset R\) such that \(\pi\) is (up to associates) the only irreducible element of \(T\) but is not a prime element of \(T\).
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 13G05
Mathematics Subject Classification ID: 13A05
Mathematics Subject Classification ID: 13F15
zbMATH DE Number: 2078849
zbMATH Keywords: prime elements
zbMATH Keywords: irreducible elements
zbMATH Keywords: factorial domains
MaRDI profile type: Publication
full work available at URL: j.jpaa.2003.10.036
OpenAlex ID: W2095140271
cites work: Factorization in commutative rings with zero divisors
cites work: On integral domains with no atoms
cites work: Q5603302
cites work: Polynomial extensions of atomic domains
DOI: 10.1016/J.JPAA.2003.10.036
description: scientific article; zbMATH DE number 2078849